Torus equivariant K-stability

Abstract

It is conjectured that to test the K-polystability of a polarised variety it is enough to consider test-configurations which are equivariant with respect to a torus in the automorphism group. We prove partial results towards this conjecture. We also show that it would give a new proof of the K-polystability of constant scalar curvature polarised manifolds.

20 pages. v2: major revision, main result changed

References in corpus (7)

• K-stability of constant scalar curvature polarization
• A stronger concept of K-stability
• Algebraicity of the Metric Tangent Cones and Equivariant K-stability
• Extremal metrics and K-stability (PhD thesis)
• K-stability of constant scalar curvature Kähler manifolds
• Extremal Kähler metrics
• Kähler-Einstein metrics along the smooth continuity method

Cited by in corpus (2)

• Orthogonal projection of a test configuration to vector fields
• Asymptotic Chow semistability implies Ding polystability for Gorenstein toric Fano varieties